An exact formula for the expected length of the minimum spanning tree of a connected graph, with independent and identical edge distribution, is given, which generalizes Steele’s formula in the uniform case. For a complete graph, the difference of expected lengths between exponential distribution, with rate one, and uniform distribution on the interval (0, 1) is shown to be positive and of rate...

Many physics experiments are designed to search for some rare, previously unseen phenomenon which would leave a distinctive event signature in the detector. Generally, there are one or more “background” processes which can mimic the signature, so that detecting the new phenomenon is a matter of observing significantly more events than would be expected from background processes. However, the Ba...

Sample-size planning historically has been approached from a power analytic perspective in order to have some reasonable probability of correctly rejecting the null hypothesis. Another approach that is not as well-known is one that emphasizes accuracy in parameter estimation (AIPE). From the AIPE perspective, sample size is chosen such that the expected width of a confidence interval will be su...

Cost-sensitive classification is based on a set of weights defining the expected cost of misclassifying an object. In this paper, a Genetic Fuzzy Classifier, which is able to extract fuzzy rules from interval or fuzzy valued data, is extended to this type of classification. This extension consists in enclosing the estimation of the expected misclassification risk of a classifier, when assessed ...

A biological model is developed here to determine the fittest attitude to risk. With a fixed environment, the type maximizing expected offspring is selected. This yields the expected utility theorem when translated into a criterion for evaluating gambles over commodities. With a random environment, however, the type selected is strictly less averse to idiosyncratic risk than to risk which is co...

In this note we essentially simplify the proof of the main result in one paper from leading computer science conference 25th ACM Symposium on Parallelism in Algorithms and Architectures (see [3].) We also present direct method and give exact asymptotic result. 1 Motivation and algorithm Consider n sensors placed randomly and independently with the uniform distribution in on the unit interval [0...

This article investigates new score and accuracy functions for ranking interval-valued intuitionistic fuzzy numbers (IVIFNs). The novelty of these functions is that they allow the comparison of IVIFNs by taking into account of the decision makers’ attitudinal character. The new attitudinal expected score and accuracy functions extend Xu and Chen’s score and accuracy degree functions, and verify...

The problem of setting a confidence interval with fixed proportional accuracy for the mean of a normal distribution is considered. A sequential procedure is proposed; and asymptotic expansions for its average coverage probabilities and its expected sample size are obtained. The procedure is shown to have asymptotically minimal expected sample size, subject to a constraint on the error probabili...

This paper develops a new performance measurement methodology for algorithmic trading. By adapting capability from the quality control literature, we present new criteria for assessing control, expected tail loss and risk-adjusted performance in a single framework. The multi-scale capability measure we present is more descriptive and more appropriate for algorithmic trading than the traditional...